Homework for Week 5
Math 408 Section A, February 2
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Reading Assignment:
- Multivariable Calculus Review: Due Wednesday, January 28.
- Optimality Conditions for Unconstrained Problems: Due Monday, February 2.
- Optimality Conditions for Constrained Problems: Due Friday, February 6.
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Homework Assignment:
- LP Primer:
- Be able to state and prove the Weak Duality Theorem for
LPs in standard form.
- LP Modeling:
- Cash flow matching problems.
- Be able to model the modeling problems
1, 2, 3, 4, and 5 as LPs.
- LP Duality:
- Be able to state the Strong Duality Theorem for
LPs in standard form.
- Be able to compute the dual of a general LP concretely specified,
i.e. with the coefficients given numerical values.
- Be able to compute the dual of a general LP abstractly specified,
i.e. in matrix notation.
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Vocabulary List:
- Linear Programming
- Linear Programming Duality
- LP Standard Form
- Weak Duality Theorem
- Proof of the Weak Duality Theorem
- Strong Duality Theorem
- Optimality Conditions for Unconstrained Problems
- First-order necessary conditions for optimality.
- Second-order necessary conditions for optimality.
- Second-order sufficient conditions for optimality.
- Convexity.
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Key Concepts:
- LP duality, weak and strong duality theorems
- LP Standard Form
- LP Duality Theory.
- LP Modeling
- Optimality Conditions
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Skills to Master:
- Computing the dual to a general LP.
- Modeling LPs
- Verifying optimality conditions.
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Quiz:
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The quiz will have two questions. The first question will be worth 30
points and will ask you to write the dual of an
arbitrary LP. This LP may be given in matrix notation form.
The second question is worth 20 points and will ask you to
model a problem as an LP.